A foliation groupoid is a Lie groupoid \(G \rightrightarrows M\)  whose space of objects \(M\)  is Hausdorff and whose isotropy groups \(G_x\)  are discrete for all \(x\in M\) . For instance, every étale Lie groupoid with Hausdorff objects manifold is a foliation groupoid. The converse is not true, however every foliation groupoid is Morita equivalent to an étale groupoid. As shown in [1]}, being a foliation groupoid is equivalent to the associated Lie algebroid anchor map \(\rho :A\rightarrow TM\)  being injective. As a consequence, the manifold \(M\)  comes with a regular foliation \(\mathcal {F}\)  tangent to the leaves of \(\mathrm {im}(\rho )\subseteq TM\) . Note that if \(G \rightrightarrows M\)  is source-connected the leaves of \(\mathrm {im}(\rho )\subseteq TM\)  coincide with the groupoid orbits.
